Differential and Integral Equations

Time-dependent nonlinear evolution equations

Chin-Yuan Lin

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Of concern is the nonlinear evolution equation \begin{align} \frac{du}{dt} & \in A(t)u,\ \ 0 < t < T \notag \\ u(0) & = u_{0} \notag \end{align} in a real Banach space $ X $, where $ A(t) : D(A(t)) \subset X \longrightarrow X $ is a time-dependent, nonlinear, multivalued operator acting on $ X $. It is shown that under certain assumptions on $ A(t) $, the equation has a strong solution. Applications to nonlinear parabolic boundary value problems with time-dependent boundary conditions are given.

Article information

Differential Integral Equations, Volume 15, Number 3 (2002), 257-270.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G25: Evolution inclusions
Secondary: 47N20: Applications to differential and integral equations


Lin, Chin-Yuan. Time-dependent nonlinear evolution equations. Differential Integral Equations 15 (2002), no. 3, 257--270. https://projecteuclid.org/euclid.die/1356060860

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